Abstract This paper details the nonlinear design of adaptive lattices by determination and enhancement of compliant modes and optimizing the designed structure for delivering high amplitude actuation. The particular focus is the kagome lattice geometry—a pattern with some unique and useful actuation properties. Developing a novel design tool, the stiffness matrix of the beam assembly is calculated using a developed second-order geometrically nonlinear beam finite element formulation allowing large rotations. Based on this formulation in conjunction with singular value decomposition of the stiffness matrix, the modal optimization technique reduces the continuous structure with many degrees of freedom to a small number of low energy modes, which form the basis of designing the adaptive structure. For delivering high-amplitude actuation, the designed structure needs to be re-optimized due to changes in the nonlinear stiffness matrix under large deformation. This is performed via Bayesian optimization and by removing some internal members of the lattice. The integrity and feasibility of the optimum design is guaranteed via defining some constraints on removed members.

中文翻译：

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晶格中高振幅驱动的柔顺模式的确定和增强

摘要 本文详细介绍了自适应晶格的非线性设计，通过确定和增强柔顺模式以及优化设计结构以提供高振幅驱动。特别关注的是 Kagome 晶格几何——一种具有一些独特且有用的驱动特性的图案。开发一种新颖的设计工具，使用开发的二阶几何非线性梁有限元公式计算梁组件的刚度矩阵，允许大旋转。基于该公式并结合刚度矩阵的奇异值分解，模态优化技术将具有多自由度的连续结构减少到少量低能量模态，这构成了设计自适应结构的基础。用于提供高振幅驱动，由于大变形下非线性刚度矩阵的变化，设计结构需要重新优化。这是通过贝叶斯优化和删除格子的一些内部成员来执行的。优化设计的完整性和可行性是通过对移除的成员定义一些约束来保证的。